Combined First and Second Order Variational Approaches for Image Processing
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  • 作者：Gabriele Steidl
  • 关键词：Mathematical image analysis ; Variational models ; Primal ; dual algorithms ; Higher order models ; Optical flow ; Strain tensor ; Cyclic proximal point algorithm ; Cyclic data ; 49J40 ; 49M29 ; 49M37 ; 49N45 ; 52A41 ; 65K10
  • 刊名：Jahresbericht der deutschen Mathematiker-Vereinigung
  • 出版年：2015
  • 出版时间：June 2015
  • 年：2015
  • 卷：117
  • 期：2
  • 页码：133-160
  • 全文大小：4,344 KB
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  • 作者单位：Gabriele Steidl (1)

    1. Dept. of Mathematics, University of Kaiserslautern, Paul-Ehrlich-Str. 31, 67653, Kaiserslautern, Germany
  • 刊物类别：Mathematics and Statistics
  • 出版者：Vieweg+Teubner Verlag
  • ISSN：1869-7135
文摘
Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like image restoration, registration, segmentation, super-resolution, and estimation of flow fields. We review recent progress in mathematical image processing by combining first and second order derivatives in the regularization term of variational models. We demonstrate the power of the proposed methods by two rather different applications. The approaches make use of two different splitting methods of the functional to obtain iterative numerical schemes which require in each step only the computation of simple proximal mappings.

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